Question

Abhinav invested a certain amount at the rate of 8 p.c.p.a. for 5 years and obtained $SI$ of $Rs.3800$. Had he invested the same amount would she have obtained as $CI$ at the end of 2 years?

Answer 1

Hint: First of all, we will find the value of principal amount invested by Abhinav by using the formula of simple interest i.e. $SI=\dfrac{P\times r\times n}{100}$ and then using that as principal amount, we will find the value of total amount Abhinav will earn after 2 years if he invests same amount for compound interest by using the formula of $CI$ i.e. $A=P{{\left( 1+\dfrac{r}{100} \right)}^{n}}$ and then from that we will find compound interest he earns by taking difference of total amount and principal amount i.e. $\text{Compound Interest}=\text{Total amount}-\text{Principal amount}$.

Complete step-by-step answer:
In question we are given that Abhinav invested a certain amount at the rate of 8 p.c.p.a. for 5 years and obtained $SI$ of $Rs.3800$ and we are asked to find the compound interest he could earn if he invests the same amount for a period of 2 years. so, first of all we will find the principal amount Abhinav invested on which he earned $SI$ which can be given by the formula of simple interest as,
$SI=\dfrac{P\times r\times n}{100}$ ………………………………….….(i)
Where, P is principal amount, r is rate of interest and n is time period.
Here, the simple interest earned is $Rs.3800$, rate of interest per annum is $8%$ and time period is 5 years, so on substituting these values in expression (i) we will get,
$3800=\dfrac{P\times 8\times 5}{100}$
On further simplifying we will get value of principal amount (P) as,
$\dfrac{3800\times 100}{5\times 8}=P$
$P=\dfrac{380000}{40}=Rs.9500$ ……………………………...…..……..(ii)
Now, using this principal amount we can find the amount which Abhinav earns at the end of 2 years if he invests for the same interest rate. So, the formula of Amount for compound interest can be given as,
$A=P{{\left( 1+\dfrac{r}{100} \right)}^{n}}$ …………………………………….……..(iii)
Where, A is total amount, P is principal amount, r is rate of interest and n is time period.
Here, the principal amount is $Rs.9500$, rate of interest is $8%$ and time period is 2 years. so, on substituting these values in expression (iii), we will get,
$A=9500{{\left( 1+\dfrac{8}{100} \right)}^{2}}$
On simplifying further, we will get,
$\Rightarrow A=9500{{\left( \dfrac{100}{100}+\dfrac{8}{100} \right)}^{2}}$
$\Rightarrow A=9500{{\left( \dfrac{108}{100} \right)}^{2}}$
$\Rightarrow A=9500\times \dfrac{11664}{10000}=Rs.11080.8$ ………………………….……..(iv)
Now, the compound interest is the difference between the total amount a person receives to that of he invested or Principal amount, which can be seen mathematically as,
$\text{Compound Interest}=\text{Total amount}-\text{Principal amount}$
$CI=A-P$
Now, on substituting the values of P and A from expression (ii) and (iv) respectively we will get,
$CI=11080.8-9500=1580.8$
Thus, compound interest earned by Abhinav is $Rs.1580.8$.

Note: Students might consider the value of Total amount earned as the value of compound interest by using the formula, $A=P{{\left( 1+\dfrac{r}{100} \right)}^{n}}$, so, by doing so the compound interest earned by Abhinav at the end becomes $Rs.11080.8$, which is wrong because interest earned can not be greater than principal amount invested. So, students must keep this in mind and use formulas correctly.